Consider $(f_n)_{n\ge 0}$ the Fibonacci sequence, defined by $f_0 = 0$, $f_1 = 1$, $f_{n+1} = f_n + f_{n-1}$ for all positive integers $n$. Solve the following equation in positive integers $$nf_nf_{n+1} = (f_{n+2} - 1)^2.$$.
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Tags: number theory, 1st edition
Consider $(f_n)_{n\ge 0}$ the Fibonacci sequence, defined by $f_0 = 0$, $f_1 = 1$, $f_{n+1} = f_n + f_{n-1}$ for all positive integers $n$. Solve the following equation in positive integers $$nf_nf_{n+1} = (f_{n+2} - 1)^2.$$.